Hi,
Have you checked engineering physics major? It covers engineering, physics, math, etc, probably will fit to you, check the courses as well before deciding.
Short story from me, Few of my friends worked as mechanical engineer and involved in multidisciplines projects. Some of my friends are from physics and they act as electrical or instrumentation engineers, they find no problem working with it and interacting with other disciplines (relating of works, of course).
However, in my experiences, it is very rare to find physics graduates in the oil & gas company, engineering / construction company, business / engineering consultant, FMCG, etc, mostly are graduates from chemical / mechanical / electrical engineering and also computer science.
Lastly, it depends on your long-term goal and your passion.
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